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MAC 1140 Exam 1 Review

Fall 2016

This review, produced by the CLAS Teaching Center, contains a collection of questions which are

representative of the type you may encounter on the exam. Other resources made available by the

Teaching Center include:

• Walk-In tutoring at Broward Hall

• Private-Appointment, one-on-one tutoring at Broward Hall

• Walk-In tutoring in LIT 215

• Supplemental Instruction

• Video resources for Math and Science classes at UF

• Written exam reviews and copies of previous exams

The teaching center is located in the basement of Broward Hall:

You can learn more about the services offered by the teaching center by visiting

https://teachingcenter.ufl.edu/

MAC 1140 Exam 1 Review

1. Sketch the following subsets of the real numbers on a number line

(a) [−4, 12)

(b) (−∞, 0]

(c) x − 3 ≤ 5

(d) x is no larger than 9.

2. Sketch the following subsets of the real numbers on a number line

(a) |x| < 2

(b) |x| ≥ 2

(c) |x − 1| > 3

(d) The distance from x to 1 is at least 2.

3. Simplify the radical expressions

√

18z 5 x7

(a) √

2zx3

√

5

(b) 64x10 − 32x5

√

√2 ·

12 + 12

2

(c)

2

4. Write each function piecewise without absolute value bars.

(a) e(x) = |x|

(b) f (x) = |2x + 1|

|10x + 8|

5x + 4

1

(d) h(x) =

|x|

(c) g(x) =

5. Expand each of the following expressions.

(a) (x + 1)2

(b) (x − 2)(x + 2)

(c) (2x − 1)3

(d) (x + y + 1)(x + y − 1)

CLAS Teaching Center

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MAC 1140 Exam 1 Review

6. Determine the requested coefficient in the expanded form of each expression below.

(a) Coefficient of x2 in (2x − 4)(1 − x)

(b) Coefficient of x in (2x + 1)2

(c) Coefficient of x3 in (2x + 3)3

(d) Coefficient of xy in (x + y − 1)(2x − 3y + 2)

7. Factor each of the following polynomials.

(a) 8y 2 (x + 3) − 2(x + 3)

(b) x4 − 4

(c) x2 + x − 6

(d) 3x2 − 6x + 3

(e) 2x2 + 5x − 3

(f) x3 − 27

(g) x3 + 3x2 − 6x − 18

8. Simplify and find the domain of each rational function.

1

(a) f (x) =

1−x

x+1

(b) g(x) = 2

x +x−6

9. Simplify each expression, leaving positive exponents only.

(a) 3x−4/3 + 2x−1/3

(b) −x−1 (1 + x2 )−2/3 − 2x−3 (1 + x2 )1/3

(c) x2 (1 − 2x)−3/2 + (1 − 2x)−1/2

(d)

−2(x2 − 3)−3 (2x)(x + 1)3 − 3(x + 1)2 (x2 − 3)−2

[(x + 1)3 ]2

(e)

(6x + 1)3 (27x2 + 2) − (9x3 + 2x)(3)(6x + 1)2 (6)

[(6x + 1)3 ]2

10. Find the domain of each of the following functions.

x−3

(a) g(x) = 2

x − 5x + 10

√

(b) h(x) = 2x + 7

CLAS Teaching Center

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MAC 1140 Exam 1 Review

11. Solve the following equations for the indicated variable.

x+2

(a) y =

for x.

x−1

(b) 4x2 − 1 = 7 for x

√

(c) 3 − 2t = t for t

(d) |x − 2| = 1 for x

√

(e) x + 31 − 9x = 5 for x

10x + 3

1

(f)

= for x

5x + 6

2

(g) (x2 − x − 22)3/2 = 27 for x

12. Solve the following inequalities.

(a) −2x + 1 ≥ 0

(b) |x − 5| + 15 > 5

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